Multicomponent gap solitons in spinor Bose-Einstein condensates

We model the nonlinear behavior of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or antiferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multicomponent structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA) frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetization, i.e., intrinsic precession of the local spin. Finally, we demonstrate that nonstationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.